Solve sqrt{1/8(18225-25/9)}

$$\sqrt{ \frac{ 1 }{ 8 } (18225- \frac{ 25 }{ 9 } ) }$$

Evaluate

$$\frac{10\sqrt{205}}{3}\approx 47.726070211$$

Solution Steps

Convert 18225 to fraction \frac{164025}{9}.

$$\sqrt{\frac{1}{8}\left(\frac{164025}{9}-\frac{25}{9}\right)}$$

Since \frac{164025}{9} and \frac{25}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{1}{8}\times \frac{164025-25}{9}}$$

Subtract 25 from 164025 to get 164000.

$$\sqrt{\frac{1}{8}\times \frac{164000}{9}}$$

Multiply \frac{1}{8} times \frac{164000}{9} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1\times 164000}{8\times 9}}$$

Do the multiplications in the fraction \frac{1\times 164000}{8\times 9}.

$$\sqrt{\frac{164000}{72}}$$

Reduce the fraction \frac{164000}{72} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{20500}{9}}$$

Rewrite the square root of the division \sqrt{\frac{20500}{9}} as the division of square roots \frac{\sqrt{20500}}{\sqrt{9}}.

$$\frac{\sqrt{20500}}{\sqrt{9}}$$

Factor 20500=10^{2}\times 205. Rewrite the square root of the product \sqrt{10^{2}\times 205} as the product of square roots \sqrt{10^{2}}\sqrt{205}. Take the square root of 10^{2}.

$$\frac{10\sqrt{205}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{10\sqrt{205}}{3}$$